Switchable capacitive elements (e.g. DTCs) may be designed as capacitor banks having parallel-connected capacitors. Individual capacitors can then be connected to the bank or isolated from the bank by means of switches. The total capacitance of such a capacitor bank is calculated essentially from the sum of the connected individual capacitors.
By way of example, such capacitor banks are used as capacitive elements of variable capacitance in impedance matching circuits in signal paths for mobile communication appliances.
A variable which characterizes a capacitor bank is the quality factor Q(ω), which is a measure of the resonant response in an AC circuit or in an RF signal line. When a capacitor bank is connected in an RF signal line, it is of great significance whether the quality factor of the bank or of the switchable capacitive element is in tune with the quality factors of the remaining RF circuit components connected thereto. Remaining circuit components may be RF filters in a front-end circuit or the antenna of a mobile communication appliance, for example.
DTCs are known from the publication WO 2009/108391. A DTC comprises a plurality of parallel paths having capacitors connected therein. The capacitances of the individual capacitors of the parallel-connected paths correspond to the powers of two of a very small capacitance. It is thus possible for 2n equidistant capacitances to be adjusted for n parallel-connected paths. Each parallel path of a DTC comprises a cascade of serially-connected semiconductor switches, which is connected in series with the capacitor. The cascade can be used to connect or isolate the capacitor of the parallel path to or from an RF signal line. WO 2009/108391 specifies rules (cf. equations 5A, 5B, 6A and 6B) for calculating the quality factor of a DTC or a parallel path on the basis of characteristic variables of the capacitors of the parallel paths and of the semiconductor switches. In this case, a distinction is drawn between open and closed semiconductor switches.
It is an object of the present invention to specify a circuit which has an improved quality factor in comparison with previously known circuits. In particular, it is an object of the invention to specify a switchable capacitive element which has an improved quality factor and which is not reliant on the use of variables for the capacitors which are based on powers of two.
The invention achieves these objects by means of switchable capacitive elements and by means of a switchable capacitance bank according to one of the independent claims. Advantageous embodiments and a method of production can be found in further claims.
One embodiment of a switchable capacitive element having an adjustable capacitance and an improved quality factor comprises n parallel-connected paths with a respective capacitor of capacitance C or 2m*C, wherein m is an integer≧0 and less than n. Per path, the switchable capacitive element comprises n semiconductor switches, cascaded in the path, with a respective source connection, gate connection and a drain connection. The switchable capacitive element has a frequency-dependent quality factor QSon(ω) when the semiconductor switches are open and has a frequency-dependent quality factor QSoff(ω) when the semiconductor switches are closed. RG is the nonreactive resistance of an external resistive element (i.e., external to the switchable capacitive element) connected to the gate connection, RGS is the nonreactive resistance between the gate connection and the source connection, RGD is the nonreactive resistance between the gate connection and the drain connection, RON is the nonreactive resistance between the drain connection and the source connection, if the semiconductor switch is closed. RD is the nonreactive resistance of an external, i.e. one that is not associated with the switch, resistive element connected between the drain connection and the source connection. rDS is the intrinsic nonreactive resistance of the switch between the drain connection and the source connection. CGD is the capacitance between the gate connection and the drain connection. CGS is the capacitance between the gate connection and the source connection. CDS is the capacitance between the drain connection and the source connection. RMIM is the (finite) nonreactive resistance of the capacitor. RMIM can be used to model the quality of the capacitor. The values C, RMIM, Ron, RG, RGS, RGD, RD, rDS, CGD, CGS, CDS are in this case optimized according to the equation
                              Q          ON          S                =                  1                      ω            ·                          (                                                R                  MIM                                +                                                                            n                      ·                                              R                        ON                                                              ⁢                                          R                      a                                                                                                  n                      ·                                              R                        ON                                                              +                                          R                      a                                                                                  )                        ·            C                                              (                  Equation          ⁢                                          ⁢          1                )            when the semiconductor switches are open and according to the equation
                              Q          OFF          S                =                  1                      ω            ·                          (                                                R                  MIM                                +                                  n                  ⁢                                                                          ⁢                                      R                    d                                                  +                                  n                                                            ω                      2                                        ⁢                                          C                      d                      2                                        ⁢                                          R                      e                                                                      +                                                      n                    3                                                                              ω                      2                                        ⁢                                          C                      d                      2                                        ⁢                                          R                      a                                                                                  )                        ·                                                                                            ⁢                                                      C                    d                                    ⁢                  C                                                                              C                  d                                +                                  n                  ⁢                                                                          ⁢                  C                                                                                        (                  Equation          ⁢                                          ⁢          2                )            when the semiconductors are closed. In this case, the auxiliary variables Ra, Rb, Rd, Cd, Re, Rc and Cc cited in the Equations 1-6 (Equations 3-6 are set forth below) are calculated from the values C, RMIM, Ron, RG, RGS, RGD, RD, rDS, CGD, CGS, CDS as follows:
                    ⁢          (              Equation        ⁢                                  ⁢        Set        ⁢                                  ⁢        1            )                  R      a        =                                        R            G                    ·                                                    C                GD                            +                              C                GS                                                    C              GD                                      ⁢                                  ⁢                  R          b                    =                                                  R              G                        ·                                                            C                  GD                                +                                  C                  GS                                                            C                GS                                              ⁢                                          ⁢                      R            d                          =                                                            R                c                                                              (                                      1                    +                                                                  C                        DS                                                                    C                        c                                                                              )                                2                                      ⁢                                                  ⁢                          C              d                                =                                                    C                DS                            +                                                C                  c                                ⁢                                                                  ⁢                                  R                  e                                                      =                                                                                                      r                      DS                                        ⁢                                          R                      D                                                                                                  r                      DS                                        +                                          R                      D                                                                      ⁢                                                                  ⁢                                  R                  c                                            =                                                                                          R                      GD                                                              1                      +                                                                        (                                                      ω                            ⁢                                                                                                                  ⁢                                                          R                              GD                                                        ⁢                                                          C                              GD                                                                                )                                                2                                                                              +                                                            R                      GS                                                              1                      +                                                                        (                                                      ω                            ⁢                                                                                                                  ⁢                                                          R                              GS                                                        ⁢                                                          C                              GS                                                                                )                                                2                                                                              -                                                            1                                                                        ω                          2                                                ⁢                                                  R                          G                                                ⁢                                                  C                          GD                                                ⁢                                                  C                          GS                                                                                      ⁢                                                                                  ⁢                                          C                      c                                                                      =                                                                                                    C                        GD                                            ⁢                                              C                        GS                                                                                                            C                        GD                                            +                                              C                        GS                                                                              .                                                                        
In this case, n is a natural number ≧1.
The indication of this dependency of the quality factor Q on the variables which characterize the switchable capacitive element provides a simple means for selecting the variables C, RMIM, RON, RG, RGS, RGD, RD, rDS, CGD, CGS and CDS such that a suitable quality factor is obtained which can be prescribed from a specification that is to be observed, for example. To this end, the optimum for the quality factor Q can be ascertained particularly by means of Monte Carlo simulations or by means of analytical or numerical calculations of the partial derivations of Q on the basis of the parameters C, RMIM, RON, RG, RGS, RGD, RD, rDS, CGD, CGS and CDS that are to be varied.
In one embodiment, the cascade of the semiconductor switches in each path is connected between the capacitor of the path and ground.
An alternative variant of the switchable capacitive element comprises n parallel-connected paths with a respective capacitor of capacitance C or 2m*C, wherein m is an integer≧0 and less than n, and per path n semiconductor switches, cascaded in the path, with a respective source connection, gate connection and drain connection. The switchable capacitive element has a frequency-dependent quality factor QDon(ω) when the semiconductor switches are open and has a frequency-dependent quality factor QDoff(ω) when the semiconductor switches are closed. RG is the nonreactive resistance of a resistive element connected to the gate connection, RGS is the nonreactive resistance between the gate connection and the source connection, RGD is the nonreactive resistance between the gate connection and the drain connection, RD is the nonreactive resistance of an external resistive element connected between the drain connection and the source connection, rDS is the nonreactive resistance between the drain connection and the source connection. CGD is the capacitance between the gate connection and the drain connection; CGS is the capacitance between the gate connection and the source connection; CDS is the capacitance between the drain connection and the source connection. The values C, RMIM, RON, RG, RGS, RGD, RD, rDS, CGD, CGS, CDS are optimized according to the equation
          ⁢                                          Q            ON            D                    =                      1                          ω              ·                              (                                                      R                    MIM                                    +                                      n                    ⁢                                                                                  ⁢                                          R                      ON                                                        +                                      n                                                                  ω                        2                                            ⁢                                              C                        2                                            ⁢                                              R                        a                                                                              +                                      n                                                                  ω                        2                                            ⁢                                              C                        MIM                        2                                            ⁢                                              R                        b                                                                                            )                            ·              C                                                            (                      Equation            ⁢                                                  ⁢            3                    )                    when the semiconductor switches are open and according to the equation
                    ⁢          (              Equation        ⁢                                  ⁢        4            )                  Q      OFF      D        =                                     ⁢              1                                                            ω                ·                                  (                                                            R                      MIM                                        +                                          n                      ⁢                                                                                          ⁢                                              R                        d                                                              +                                          n                                                                        ω                          2                                                ⁢                                                  C                          d                          2                                                ⁢                                                  R                          e                                                                                      +                                          n                                                                        ω                          2                                                ⁢                                                  C                          2                                                ⁢                                                  R                          a                                                                                      +                                          n                                                                                                                                  ω                              2                                                        ⁡                                                          (                                                                                                C                                  ⁢                                                                                                                                          ⁢                                                                      C                                    d                                                                                                                                                                        n                                    ⁢                                                                                                                                                  ⁢                                    C                                                                    +                                                                      C                                    d                                                                                                                              )                                                                                2                                                ⁢                                                  R                          b                                                                                                      )                                ·                                                                                                                                                                  ⁢                                      C                    ⁢                                                                                  ⁢                                          C                      d                                                                                                            n                    ⁢                                                                                  ⁢                    C                                    +                                      C                    d                                                                                          when the semiconductor switches are closed. n is a natural number ≧1. The auxiliary variables Ra, Rb, Rd, Re, and Cd are calculated from the values C, RMIM, Ron, RG, RGS, RGD, RD, rDS, CGD, CGS, CDS as set forth above in Equation Set 1.
In one embodiment of this variant, the capacitor of each path is connected between the cascade of the semiconductor switches and ground.
The embodiments cited above are thus distinguished in that in one case the cascade of the semiconductor switches is connected to ground and that in the other case the capacitor is connected to ground. It is preferred if the cascade of the semiconductor switches is connected between the capacitor of a path and ground.
A further alternative embodiment of the invention relates to a switchable capacitance bank having m switchable capacitive elements. Each of the switchable capacitive elements comprises n parallel-connected paths with a respective capacitor of capacitance am*C and per path n semiconductor switches, cascaded in the path, with a respective source connection, gate connection and drain connection. In this case, a is a real number >1. Each path comprises n semiconductor switches, cascaded in the path, with a respective source connection, gate connection and drain connection. In this case, the capacitors of each path are connected between the cascade of the semiconductor switches and ground. The switchable capacitive element has a frequency-dependent quality factor Qon(ω) when the semiconductor switches are open and has a frequency-dependent quality factor Qoff(ω) when the semiconductor switches are closed. RG is the nonreactive resistance of a resistive element connected to the gate connection, RGS is the nonreactive resistance between the gate connection and the source connection, RGD is the nonreactive resistance between the gate connection and the drain connection, RD is the nonreactive resistance of an external resistive element connected between the drain connection and the source connection, rDS is the nonreactive resistance of the switch between the drain connection and the source connection. CGD is the capacitance between the gate connection and the drain connection, CGS is the capacitance between the gate connection and the source connection, CDS is the capacitance between the drain connection and the source connection. In this case, the values C, RMIM, RON, RG, RGS, RGD, RD, rDS, CGD, CGS, CDS are optimized according to the equation
                              Q          ON                =                  1                      ω            ·                          (                                                                    1                    a                                    ⁢                                      R                    MIM                                                  +                                                                            n                      ·                                              1                        a                                                              ⁢                                                                  R                        ON                                            ·                                              1                        a                                            ·                                              R                        a                                                                                                                                                n                        ·                                                  1                          a                                                                    ⁢                                              R                        ON                                                              +                                                                  1                        a                                            ⁢                                              R                        a                                                                                                        )                        ·            a            ·            C                                              (                  Equation          ⁢                                          ⁢          5                )            when the semiconductor switches are open and according to the equation
                    ⁢          (              Equation        ⁢                                  ⁢        6            )                  Q      OFF        =                                     ⁢              1                                                            ω                ·                                  (                                                                                    1                        a                                            ⁢                                              R                        MIM                                                              +                                          n                      ⁢                                              1                        a                                            ⁢                                                                                          ⁢                                              R                        d                                                              +                                          n                                                                        ω                          2                                                ⁢                                                  a                          2                                                ⁢                                                  C                          d                          2                                                ⁢                                                  1                          a                                                ⁢                                                  R                          e                                                                                      +                                                                  n                        3                                                                                              ω                          2                                                ⁢                                                  a                          2                                                ⁢                                                  C                          d                          2                                                ⁢                                                  1                          a                                                ⁢                                                  R                          a                                                                                                      )                                ·                                                                                                                                                                  ⁢                                      a                    ⁢                                                                                  ⁢                                                                  C                        d                                            ·                      a                      ·                                                                                          ⁢                      C                                                                                                            a                    ⁢                                                                                  ⁢                                          C                      d                                                        +                                                            n                      ·                                                                        a                          ⁢                                                                                                                                2                                                              ⁢                    C                                                                                          when the semiconductor switches are closed. n and m are integers ≧0. n is ≧1. In this case, the auxiliary variables Ra, Rd, Re, and Cd cited in the Equations 5-6 are calculated from the values C, RMIM, Ron, RG, RGS, RGD, RD, rDS, CGD, CGS, CDS as set forth in Equation Set 1 above.
In one embodiment, the values C, RMIM, RON, RG, RGS, RGD, RD, rDS, CGD, CGS and CDS are chosen such that the ratio comprising the quality factor Q and the sum of the intrinsic capacitances CGD, CGS and CDS, namely
      Q                  C        GD            +              C        GS            +              C        DS              ,is at a maximum. In that case, the switchable capacitive element has a minimized surface area requirement.
The switchable capacitive element may be part of a filter circuit.
Methods according to the invention for producing adjustable capacitive elements or capacitance banks comprise the following:
a target quality factor for the element or for the bank is ascertained or prescribed,
the magnitude of the capacitances of the capacitors of the paths is ascertained,
the values of the variables C, RMIM, RON, RG, RGS, RGD, RD, rDS, CGD, CGS and CDS are ascertained according to the aforementioned equations. For example, the target quality factor can be optimized according to a function that includes a resistance Ra whose value is calculated from a nonreactive resistance RG of an external resistive element connected to the gate connection (G), a gate-drain capacitance CGD between the gate connection and the drain connection, and a gate-source capacitance CGS between the gate connection and the source connection.
Optionally, a method comprises the readjustment of the magnitude of the capacitances of the capacitors in the paths, and the implementation of the adjustable capacitive elements or capacitance banks by proportioning the parameters in accordance with the ascertained values.